J. McCalley

Transient frequency performance and wind penetration

Content

1. Motivation2. Power balance-frequency basics3. Frequency Performance Analysis

2

Motivation• In many parts of the country, wind and/or solar is increasing.• Fossil-based generation is being retired because

– There is significant resistance to coal-based plants due to their high CO2 emission rates.

– There are other environmental concerns, e.g., once-through cooling (OTC) units in California and the effects of EPA’s Cross-state air pollutions rules (CSAPR) and Mercury and Air Toxic Standards (MATS) (also known as Maximum Achievable Control Technology, MACT). For CSAPR effects, see, e.g., www.powermag.com/POWERnews/4011.html (Texas shut downs) and for CSAPR/MATS effects, see the next slide. For OTC effects, see www.world-nuclear-news.org/RS-California_moves_to_ban_once_through_cooling-0605105.html, http://www.caiso.com/1c58/1c58e7a3257a0.html, and next-next slide.

• Fossil-based generation contributes inertia. Wind and solar do not contribute inertia, unless they are using inertial emulation.

• Inertia helps to limit frequency excursions when power imbalance occurs.

Decreased fossil w/ increased wind/solar creates trans freq risk.3

Potential effects of CSAPR/MATS

4Source: A. Saha, “CSAPR & MATS: What do they mean for electric power plants?” presentation slides at the 15 th Annual Energy, Utility, and Environmental Conference, Jan 31, 2012, available at www.mjbradley.com/sites/default/files/EUEC2012_Saha_MATS-CSAPR.pdf.

Once-through cooling units in S. California

5

There are 8 plants (26 units) that are impactedTotal potential MW capacity at risk = 7,416 MW.

Load center

New wind and solar generation due to Cal requiring 33% by 2020.

Summary of power balance control levels

No. Control Name Time frame Control objectives Function

1 Inertial response 0-5 secsPower balance and

transient frequency dip minimization

Transient frequency control

2 Primary control, governor 1-20 secs

Power balance and transient frequency

recovery

Transient frequency control

3 Secondary control, AGC

4 secs to 3 mins

Power balance and steady-state frequency Regulation

4 Real-time market Every 5 mins Power balance and economic-dispatch

Load following and reserve provision

5 Day-ahead market Every day Power balance and

economic-unit commitmentUnit commitment and

reserve provision

6

Frequency Study Basics• Inertia The greater the inertia, the less acceleration will be

observed and the less will be the frequency deviation. Inertia is proportional to the total rotating mass.

• Primary Control Senses shaft speed, proportional to frequency, and modifies

the mechanical power applied to the turbine to respond to the sensed frequency deviations.

7

auPtH

)(2

Re

First 2 Levels of Frequency Control• The frequency declines from t=0 to about t=2 seconds. This frequency decline is due to

the fact that the loss of generation has caused a generation deficit, and so generators decelerate, utilizing some of their inertial energy to compensate for the generation deficit.

• The frequency recovers during the time period from about t=2 seconds to about t=9 seconds. This recovery is primarily due to the effect of governor control (also, underfrequency load shedding also plays a role).

• At the end of the simulation period, the frequency has reached a steady-state, but it is not back to 60 Hz. This steady-state frequency deviation is intentional on the part of the governor control and ensures that different governors do not constantly make adjustments against each other. The resulting steady-state error will be zeroed by the actions of the automatic generation control (AGC).

8 / 12

Source: FERC Office of Electric Reliability available at: www.ferc.gov/EventCalendar/Files/20100923101022-Complete%20list%20of%20all%20slides.pdf

9

This is load decrease, shown here as a gen increase.

First 2 Levels of Frequency Control – another look

First 3 Levels of Frequency Control

The Sequential Actions of frequency control following the sudden loss of generation and their impact on system frequency

10 / 12

Renewable Integration Effects on Frequency

• Reduced inertia, assuming renewables do not have inertial emulation• Decreased primary control (governors), assuming renewables do not

have primary controllers• Decreased secondary control (AGC), assuming renewables are not

dispatchable.• Increased net load variability, a regulation issue• Increased net load uncertainty, a unit commitment issue

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Our work in these slides is about the first two bullets.

Transient frequency control

A power system experiences a load increase (or equivalently, a generation decrease) of ∆PL at t=0, located at bus k. At t=0+, each generator i compensates according to its proximity to the change, as captured by the synchronizing power coefficient PSik between units i and k, according to

12

Ln

jSkj

Sikn

jSkj

LSikei P

P

P

P

PPP

11

0ikik

ikSik

PP

Equation (1) is derived for a multi-machine power system model where each synchronous generator is modeled with classical machine models, loads are modeled as constant impedance, the network is reduced to generator internal nodes, and mechanical power into the machine is assumed constant. Then the linearized swing equation for gen i is …

(1)

Transient frequency control

Bring Hi over to the right-hand-side and rearrange to get:

13

eiii P

dt

dH

2

2

Re

2

(2)

For a load change PLk, at t=0+, substituting (1) into the right-hand-side of (2):

Ln

jSkj

Sikii PP

P

dt

dH

1

2

2

Re

2 (3)

n

jSkj

L

i

Siki

P

P

H

P

dt

d

1

2

2

Re

2 (4)

For PL>0, initially, each machine will decelerate but at different rates, according to PSik/Hi.

3

2 ,2

1

B

iiRi S

WHJW

KE in MW-sec of turb-gen set, when rotating at ωR

Transient frequency control Now rewrite eq. (3) with Hi inside the differentiation, use i instead of i, write it for all generators 1,…,n, then add them up. All Hi must be given on a common base.

14

n

jSkj

Snknn

Ln

jSkj

kS

P

P

dt

dH

PP

P

dt

dH

1

Re

1

111

Re

2

2

(5a)

LLn

jSkj

n

iSikn

i

ii PPP

P

dt

dH

1

1

1Re

2 (5b)

We will come back to this equation (5b).

Transient frequency control Now define the “inertial center” of the system, in terms of angle and speed, as

15

• The weighted average of the angles:

n

ii

n

iii

H

H

1

1

n

ii

n

iii

H

H

1

1

or (6)

• The weighted average of the speeds:

n

ii

n

iii

H

H

1

1

or

n

ii

n

iii

H

H

1

1

Differentiating with respect to time, we get…

(7)

Transient frequency control

n

ii

n

i

ii

H

dt

Hd

dt

d

1

1

(8)

Solve for the numerator on the right-hand-side, to get:

dt

dH

dt

Hd n

ii

n

i

ii 11

(9)

Now substitute (9) into (5b) to get:

L

n

ii P

dt

dH

1Re

2L

n

i

ii Pdt

dH

1Re

2 (5b) (10)

16

Transient frequency control

Bring the 2*(summation)/ωRe over to the right-hand-side:

L

n

ii P

dt

dH

1Re

2 (10)

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mH

P

dt

dn

ii

L

1

Re

2

(11a)

Eq. (11a) gives the average deceleration of the system, m, the initial slope of the avg frequency deviation plot vs. time. This has also been called the rate of change of frequency (ROCOF) [*]. All Hi (units of seconds) must be given on a common power base for (11a) to be correct. In addition -∆PL should be in per-unit, also on that same common base, so that -∆PL/2 ΣHi is in pu/sec, and mω=-∆PL ωRe/2 ΣHi is in rad/sec/sec. Alternatively,

[*] G. lalor, A. Mullane, and M. O’Malley, “Frequency control and wind turbine technologies,” IEEE Trans. On Power Systems, Vol. 20, No. 4, Nov. 2005.

fn

ii

L mH

fP

dt

fd

1

Re

2(11b)Units of Hz/sec

Transient frequency control

fn

ii

G mH

fP

dt

fd

1

Re

2

Consider losing a unit of ∆PG at t=0. Assume:•There is no governor action between time t=0+ and time t=t1 (typically, t1 might be about 1-2 seconds). •The deceleration of the system is constant from t=0+ to t=t1. The frequency will decline to 60-mft1. The next slide illustrates.

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Transient frequency control

fn

ii

G mH

fP

dt

fd

1

Re

2

The greater the ROCOF following loss of a generator ∆PG, the lower will be the frequency dip. •ROCOF increases as total system inertia ΣHi decreases.•Therefore, frequency dip increases as ΣHi decreases.

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60

t1

mf1

mf2

mf3

Time (sec)

Frequency(Hz)

60-mf1t1

60-mf2t1

60-mf3t1

Frequency Basics

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• Aggregation– Network frequency is close to uniform throughout the inter-

connection during the 0-20 second time period of interest for transient frequency performance.

– For analysis of average frequency, the inertial and primary governing dynamics may be aggregated into a single machine.

– This means the interconnection’s (and not the balancing area’s) inertia is the inertia of consequence when gen trips happen.

Inertia and primary control from solar PV and wind

FUEL Steam Boiler

Generator

CONTROL SYSTEM

Steam valve control

Fuel supply control

MVARvoltage control

only

Wind speed

Gear Box

Generator

CONTROL SYSTEM

MVARvoltage control

Real power output control

STEAM-TURBINE

WIND-TURBINE

Mechanical power control

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Inertia and primary control from solar PV and wind

• A squirrel-cage machine or a wound-rotor machine (types 1 and 2) do contribute inertia.

• DFIG and PMSG wind turbines (types 3 and 4) and Solar PV units cannot see or react to system frequency change directly unless there is an “inertial emulation” function deployed, because power electronic converters isolate wind turbine/solar PV from grid frequency.No inertial response from normal control methods of wind & solar

• Neither wind nor solar PV use primary control capabilities today.

• There is potential for establishing both inertial emulation and primary control for wind and solar in the future, but so far, in North America, only Hydro Quebec is requiring it.

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Transient frequency control

fn

ii

G mH

fP

dt

fd

1

Re

2

So what is the issue with wind types 3,4 & solar PV….?1.Increasing wind & solar PV penetrations tend to displace (decommit) conventional generation.2.DFIGs & solar PV, without special control, do not contribute inertia. This “lightens” the system

(decreases denominator) •DFIGs & solar PV, without special control, do not have primary control capability. This causes frequency response degradation along with other effects (e.g., increased deadband, sliding pressure controls, blocked governor, use of power load controllers, change in load frequency response)

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Frequency Governing Characteristic, β

24

“If Beta were to continue to decline, sudden frequency declines due to loss of large units will bottom out at lower frequencies, and recoveries will take longer.”

Source: J. Ingleson and E. Allen, “Tracking the Eastern Interconnection Frequency Governing Characteristic,” Proc. of the IEEE PES General Meeting, July 2010.

Hz) (MW/0.1 f

P

The above is eastern interconnection characteristic. Decline is not caused by wind/solar. However, IF…•wind/solar displaces conventional units having inertia and having primary control•wind/solar does not have appropriate control.THEN wind/solar will exacerbate decline in β.

Potential Impacts of Low Frequency Dips• f<59.0 Hz can impact turbine blade life.• Gens may trip an UF relay (59.94 Hz, 3 min; 58.4, 30 sec; 57.8, 7.5 sec; 57.3, 45 cycles; 57 Hz, instantaneous)• UFLS can trip interruptible load (59.75 Hz) and 5 blocks (59.1, 58.9, 58.7, 58.4, 58.3 Hz)• Can violate WECC criteria:

25

25

Some illustrations

26

Crete

27

In 2000, the island of Crete had only 522 MW of conventional generation [*]. One plant has capacity of 132 MW. Let’s consider loss of this 132 MW plant when the capacity is 522 MW. Then remaining capacity is 522-132=400 MW. If we assume that all plants comprising that 400 MW have inertia constant (on their own base) of 3 seconds, then the total inertia following loss of the 132 MW plant, on a 100 MVA base, is[*] N. Hatziargyriou, G. Contaxis, M. Papadopoulos, B. Papadias, M. Matos, J. Pecas Lopes, E. Nogaret, G. Kariniotakis, J. Halliday, G. Dutton, P. Dokopoulos, A. Bakirtzis, A. Androutsos, J. Stefanakis, A. Gigantidou, “Operation and control of island systems-the Crete case,” IEEE Power Engineering Society Winter Meeting, Volume 2, 23-27 Jan. 2000, pp. 1053 -1056.

12100

3*400

1

n

iiH

Then, for ∆PL=132/100=1.32 pu, and assuming the nominal frequency is 50 Hz, ROCOF is:

sec/75.212*2

)50(32.1

21

Re HzH

fP

dt

fdm

n

ii

Lf

If we assume t1=2 seconds, then ∆f=-2.75*2=-5.5 Hz, so that the nadir would be 50-

5.5=44.5Hz! For a 60 Hz system, then mf=-3.3Hz/sec, ∆f=-3.3*2=-6.6 Hz, so that the nadir would be 60-6.6=53.4 Hz.

Ireland

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Reference [*] reports on frequency issues for Ireland. The authors performed analysis on the 2010 Irish system for which the peak load (occurs in winter) is inferred to be about 7245 MW. The largest credible outage would result in loss of 422 MW. We assume a 15% reserve margin is required, so that the total spinning capacity is 8332 MW. Consider this 422 MW outage, meaning the remaining generation would be 8332-422=7910MW.The inertia of the Irish generators is likely to be higher than that of the Crete units, so we will assume all remaining units have inertia of 6 seconds on their own base. Then the total inertia following loss of the 422 MW plant, on a 100 MVA base, is

Then, for ∆PL=422/100=4.32, and assuming the nominal frequency is 50 Hz, ROCOF is:

Assuming t1=2.75 seconds, then ∆f=-0.227*2.75=-0.624 Hz, so that the nadir is 50-0.624=49.38Hz. The figure [*] illustrates simulated response for this disturbance.

[*] G. lalor, A. Mullane, and M. O’Malley, “Frequency control and wind turbine technologies,” IEEE Trans. On Power Systems, Vol. 20, No. 4, Nov. 2005.

475100

6*7910

1

n

iiH

sec/227.0475*2

)50(32.4

21

Re HzH

fP

dt

fdm

n

ii

Lf

49.35

Nadir2.75 sec

Reasons why computed nadir is lower than simulated one

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• Governors have some influence in the simulation that is not accounted for in the calculation.

• Some portion of the load is modeled with frequency sensitivity in the simulation, and this effect is not accounted for in the calculation.

Contingencies• Category C disturbance

i. Loss of large amounts of generation via two units at a single power plant

• Category D disturbancei. Loss of large amounts of generation via three units at a single power

plantii. Loss of the California-Oregon Interface (COI) followed by activation of

the NE/SE islanding schemeiii. Loss of large amounts of generation simultaneous with a reduction in

solar or wind power output • The category (C or D) is indicated in a small box below lower left-

hand corner of each plot. Remember:– Category B minimum freq dip is 59.6 Hz.– Category C minimum freq dip is 59.0 Hz. – Category D does not have a minimum– Category “D-” indicates it is a particularly unlikely, but

severe event 30

Some additional issues• Spinning reserve levels affect on-line inertia and therefore results of transient

freq performance• Solar-PV is “inertial-less.” Solar-thermal is not. • Underfrequency load shedding can activate for “worse” initial freq performance

and make it look better at 10 secs.• Severe voltage decline can reduce power consumption and improve freq

performance.• The contingency selected has much effect.

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fn

ii

G mH

fP

dt

fd

1

Re

2

o 2 units have greater ΔPG but less restrictive criterion.

o What about loss of 2 units AND large wind or solar ramp?

o Islanding may be worst one. Why?

Reduced inertia and governing capability in SCE area (33% renewable for SCE in 2020)

Nadir is around 59.82 / 59.74 Hz for reduced inertia in SCE area when Loss of two Palo Verde units (2800MW in total)

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C: 59.0HzC: 59.0Hz

Off-Peak CaseOff-Peak Case

Peak CasePeak Case

Reduced inertia and governing capability in WECC area

• Less Inertia causes steeper drop of frequency

• Loss of 3 PV units, nadir is about 59.72/ 59.68 Hz for Peak/Off-Peak case

33

Peak CasePeak Case

Off-Peak CaseOff-Peak Case

DD

DD

Less Reserve

34

DD

DD

• Less Reserve causes slower restoration of frequency, lower post-contingency frequency

• Loss of 3 PV units, nadir is about 59.71/ 59.68 Hz for Peak/Off-Peak case

Peak CasePeak Case

Off-Peak CaseOff-Peak Case

Lower Inertia/Governor Capability and Less Reserve

35

Off-Peak CaseOff-Peak Case

• Less Inertia and Less Reserve causes faster drop and slower restoration of frequency, lower post-contingency frequency

• Loss of 3 PV units, nadir is about 59.67 Hz for Off-Peak case

DD

Interaction Between Voltage Stability and Frequency Stability-Loss of 2 Songs

36

C: 59.0HzC: 59.0Hz

• Lower Inertia case has better frequency performance for loss of 2 Songs units in load center area

• Voltage sensitive load influences frequency response positively (“less” load for lower inertia case)

Peak CasePeak Case

37

C: 59.0HzC: 59.0Hz

Peak CasePeak Case

• Put SVC near Songs Units, Frequency performance become worse than the case without SVC, for loss of 2 Song Units

Interaction Between Voltage Stability and Frequency Stability-Loss of 2 Songs

NE/SE Separation- Peak Case is studied

• Less Inertia and primary control in each island

• For peak case, there is 4719 MW of power flow on those lines which are part of the separation scheme.

• For off-peak case, there are only 1405 MW.

• Only Peak Case is studied

38

NE/SE Separation- Frequency of South Island

• Lower Inertia or less reserve causes bigger ROCOF, which leads to more load shedding (2000MW more) and higher post-Frequency

39

Peak CasePeak Case

Peak Case with Lower Inertia

Peak Case with Lower Inertia

Peak CasePeak Case

Peak Case with Less Reserve

Peak Case with Less Reserve

D-D-

NE/SE Separation- Frequency of South Island

40

Peak CasePeak Case

Peak Case with Lower Inertia and Less Reserve

Peak Case with Lower Inertia and Less Reserve

D-D-• Lower Inertia and less reserve causes bigger ROCOF, which

leads to more load shedding and higher post-Frequency

Renewable Ramp Down Together with Loss of 1 PV Unit

Simulation Conditions:– Max-solar case (Peak)– Disable all automatic load shedding in dynamic

data– In 0.1 s, turn off 3300 MW renewable( 1500 wind

+ 1800 Solar)– At 0.1s, shut down 1 Palo Verde unit– Lower Inertia and Lower governor ( only for one

case)

41

Renewable ramp down with loss of 1 PV unit

42

Peak CasePeak Case

Ramp DownRamp Down

Ramp Down + 1PV

Ramp Down + 1PV

Ramp Down+1 PV+ Lower Inertia and

Less Reserve

Ramp Down+1 PV+ Lower Inertia and

Less Reserve

B-: 59.6HzB-: 59.6Hz

• Lower nadir is about 59.63Hz at 500KV bus

Renewable ramp down with loss of 1 PV unit

Frequency on different load buses (Ramp down renewable and loss of 1 biggest unit with lower inertia and lower governor), Load shedding is disabled.

Below 59.6 Hz for more than 6 cycles (0.1s)

43

B-: 59.6HzB-: 59.6Hz

Replace CST with solar PV and Reduce Reserve

• Change all solar thermal units to solar PV in dynamic models

• Reduce reserve level to 5% from 18% for solar PV case by decreasing Pmax at SCE/WECC

Or Shutdown conventional units to reduce

reserve level to 10%

44

Change all solar thermal to solar PV in dynamic models for islanding

• Max-solar case under NE/SE islanding contingency, all Solar PV case is with less Inertia and less governor

45

Max-Solar Case with CST

Max-Solar Case with CST

Max-Solar Case with all Solar PVMax-Solar Case with all Solar PV

All Solar PV model and Less Reserve in SCE or WECC

• NE/SE islanding contingency.• Circle Red—with all solar PV model and reserve is reduced to 5% in area SCE.• Star green— with all solar PV model and reserve is reduced to 5% in WECC for max-solar case.

46

Peak Case with all Solar PV+5% Reserve in SCE

Peak Case with all Solar PV+5% Reserve in SCE

Peak Case with all Solar PV+5% Reserve in WECCPeak Case with all Solar PV+5% Reserve in WECC

All Solar PV model and Two Ways to Change Reserve

• Circle Red—with all solar PV model and 5% reserve in area SCE,• Star green— with all solar PV model and 5% reserve in WECC,• Square Brown-- with all solar PV model and 10% reserve in SCE by shutting off units for max-solar case under NE/SE islanding contingency.

47

Peak Case with all Solar PV+5% Reserve in SCE

Peak Case with all Solar PV+5% Reserve in SCE

Peak Case with all Solar PV+5% Reserve in WECCPeak Case with all Solar PV+5% Reserve in WECC

Peak Case with all Solar PV+10% Reserve in SCEPeak Case with all Solar PV+10% Reserve in SCE